SOLUTION: People living in Fairbanks drink 3600 cups of hot chocolate per day when the temperature is 0 degrees celsius. For each rise of 1 degrees celsius, their consumption decreases by 30

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Question 677031: People living in Fairbanks drink 3600 cups of hot chocolate per day when the temperature is 0 degrees celsius. For each rise of 1 degrees celsius, their consumption decreases by 30 cups per day.
a. What expression can be used to represent the number of cups of hot chocolate drunk per day as a function of degrees celsius?
b. How many cups would they drink at 5 degrees celsius?
c. How many cups would they drink at 25 degrees celsius?
d. Write an equation to determine the temperature if 3000 cups of hot chocolate were consumed in a day.
e. Solve the equation to find the temperature if 3000 cups of hot chocolate were consumed in a day.
f. Is this answer reasonable? Explain.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
We need to name/define variables:
y = number of cups of hot chocolate consumed in a day in Fairbanks.
x = temperature in degrees Celsius

"For each rise of 1 degrees celsius, their consumption decreases by 30 cups per day."
That tells you that y is a linear function of x, so we should be able to write it as
y=mx%2Bb with some constants for slope, m, and y-intercept, b.
It also tells you that the slope is m=-30.

"People living in Fairbanks drink 3600 cups of hot chocolate per day when the temperature is 0 degrees celsius."
That gives you the value of y when x=0, which is the y-intercept,
b=3600

a. The expression that represents the number of cups of hot chocolate drunk per day as a function of degrees celsius is
highlight%28y=-30x%2B3600%29 or the equivalent highlight%28y=3600-30x%29

b. How many cups would they drink at 5 degrees celsius?
x=5 --> y=3600-30%2A5 --> y=3600-150 -->
highlight%28y=3450%29

c. How many cups would they drink at 25 degrees celsius?
x=25 --> y=3600-30%2A25 --> y=3600-750 -->
highlight%28y=2850%29

d. Write an equation to determine the temperature if 3000 cups of hot chocolate were consumed in a day.
y=3000 --> highlight%283000=3600-30x%29

e. Solve the equation to find the temperature if 3000 cups of hot chocolate were consumed in a day.
--> 3000=3600-30x --> 3000-3000%2B30x=3600-30x-3000%2B30x --> 30x=600 --> 30x%2F30=600%2F30 --> highlight%28x=20%29
f. Is this answer reasonable? Explain.
It is very highlight%28reasonable%29.
At 0%5EoC they drink 3600 cups.
As the temperature increases, hot chocolate consumption decreases.
At 5%5EoC they drink less hot chocolate: 3450 cups.
Since 20%5EoC is even warmer,
they should drink even less at 20%5EoC,
but not as little as the 2850 cups they drink on those very warm 25%5EoC days.